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A rectangle has sides represented by vectors A (2,3) and B (-6,4). Determine the perimeter of the rectangle.
Do I find the answer by calculating the magnitude of OA and OB?
Thanks!
Thank you so much. The method my teacher used was really confusing me. Yours is MUCH clearer. Thanks!
How fast is the volume of a cone increasing when the radius of its base is 2cm and growing at a rate of 0.4cm/s and is height is 5 cm and growing at a rate of 0.1 cm/s?
Help!
Perfect! That's approximately the answer I got as well. Thanks a lot!
Car A is traveling north at 80 km/hr and car B is traveling west at 110 km/hr. Both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 0.4 km and car B is 0.7 km from the intersection?
I solved this problem and I think I have the correct answer, but I would love some validation!
f(x)= (2x^3+1)^2
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(4x^2-1)^3
I used the quotient rule and the chain rule, but I'm not sure how to simplify it.
I end up with:
f(x) 2(2x^3+1)(6x^2)(4x^2-1) - (2x^3+1)^2(3)(8x)
---------------------------------------------------------
(4x^2-1)^4
I factored out (4x^2-1), but can I simplify further? Thanks!
Determine the slope of the tangent to the graph of y=2x^2+3x at the general point whose x coordinate is a.
I have to use limits to solve this problem and I'm having trouble with the algebra involved. This is where I'm stuck:
lim 2x^2+3x-(2a^2-3a)
x->a x-a
Do I factor out the x and then factor out the a? Or do I factor out the 2 from the 2x^2 and the 2a^2 and then the 3 from the 3x^2 and 3a^2? I know the answer is 4x-3, I'm just having trouble getting there. Thanks!
Oops that was a typo! I forgot the x in my function. Thank you very, very much!
I'm trying to find the slope of the tangent when x is a. How do I simplify this?
y=2x^2+3
x=a
lim x->a f(x) - f(a)/x-a
lim x->a 2x^2-3x-(2a^2-3a)
----------------------
x-a
I can't thank you enough! I was so close to having the answer, I just neglected to change a-x to -(x-a) in the numerator. I was just wondering, for part 2 of the problem...when x=1/4, for example, does that value get substituted for 1/x so the equation would be
1/4-1/a
--------
1/4-a
Thanks again!
I am having a lot of difficulty with this question. I have tried for hours upon hours and even though I can get the answer using the derivative, I can't seem to get it using limits.
Here is the question:
Determine the slope of the tangent to the graph y=1/x at the general point whose x coordinate is a. Then, using the formula from part a), determine the slopes of the tangents to the graph at the points whose x coordinates are 1/4, 1/3, 1/2, 1 and 2.
I have to answer the question using the formula m=lim x->a f(x)-f(a)/x-a.
I would really really appreciate some help here! I think 1/x gets substituted for f(x), and then does 1/a get substituted for f(a)? Help!
Thanks!
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